A home for sale in Leucadia, Calif. is shown. U.S. home prices increased in November compared with a year ago, pushed higher by rising sales and a tighter supply of available homes.

WASHINGTON — U.S. home prices accelerated in November compared with a year ago, pushed higher by rising sales and a tighter supply of available homes.

The Standard & Poor’s/Case-Shiller 20-city home price index rose 5.5 percent in November compared with the same month a year ago. That’s the largest year-over-year gain in six years.

All but one of the cities in the index posted annual gains. The largest gain was in Phoenix, where prices jumped nearly 23 percent. It was followed by San Francisco, where prices rose 12.7 percent, and Detroit, where they increased 11.9 percent.

New York was the only city to report a drop from a year ago.

Prices also rose in 10 of the cities measured by the index in November from October. That’s up from seven in October from September. The biggest monthly gains were in San Francisco, Phoenix and Minneapolis.

Monthly prices are not seasonally adjusted and frequently decline over the winter. The 20-city index dipped in November from the previous month.

Steady price increases should help fuel the housing recovery. They encourage more people to buy before prices rise further. Higher prices also build homeowners’ wealth, which can spur more spending and economic growth.

The data “show a broad-based recovery in housing activity and prices across the country,” said Michael Gapen, an economist at Barclays Capital. “We expect this housing recovery to continue in the coming years.”

The S&P/Case-Shiller index covers roughly half of U.S. homes. It measures prices compared with those in January 2000 and creates a three-month moving average. The November figures are the latest available.

The index began to show annual gains in June and have been larger each month since. Prior to that, the index had fallen for 20 straight months.

Despite the increases, prices nationwide are still about 30 percent below the peak they reached at the height of the housing bubble in the summer of 2006. They are now at the same level as in the fall of 2003.

Purchases of previously occupied homes rose last year to their highest level in five years. The National Association of Realtors forecasts that sales will rise 9 percent this year. Independent economists have similar forecasts.

Sales of new homes also rose in 2012, although they remain near depressed levels.

Stable job gains and record-low mortgage rates have encouraged more people to buy homes. And the limited inventory of homes for sale has made builders more confident to step up construction. The number of previously occupied homes has fallen to an 11-year low.

Millions of homeowners still owe more on their mortgages than their homes are worth, making it difficult for them to sell. That’s one reason the supply of homes is so tight. But higher home values are lowering the number of those “under water” and should encourage more homeowners to put their homes on the market.

More people are also moving out on their own after living with friends and relatives in the recession. That’s driving a big gain in apartment construction and also pushing up rents. Higher rents are encouraging investors to buy homes and rent them.

The tighter supply of homes pushed builders in December to start work on the most homes in 4 ½ years. Last year was the best year for residential construction 2008, just after the recession started.

Home builders are also benefiting from the rebound. D.R. Horton Inc. said Tuesday that its profit in the three months ended in December more than doubled and orders jumped 39 percent.

“D.R. Horton is the best positioned it has been in its 35-year history,” chief executive Donald Horton said. “We are looking forward to the spring selling season with optimism.”